U.S. President Donald Trump has praised Ukraine for making "good progress" amid difficult conditions sparked by Russia’s annexation of the Crimea Peninsula.

Trump met his Ukrainian counterpart, Petro Poroshenko, on the sidelines of the United Nations General Assembly in New York on September 21.

"I wouldn't say it's the easiest place to live" but "it's getting better and better on a daily basis. I do hear very good things. Ukraine is coming along pretty well," Trump told Poroshenko in front of reporters before the start of their private meeting.

Speaking in English, Poroshenko said he believed that the two countries had improved security and economic cooperation.

He followed those comments in a televised briefing by saying the two leaders had a shared vision on a "new level" of defense cooperation.

"We discussed all areas of this cooperation, including cooperation with the Defense Ministry and other institutions," he added, saying the meeting with Trump last an hour. He did not say whether there had been any progress on a defensive-weapons initiative.*

The United States has imposed sanctions on Moscow for its activities in Ukraine, including the annexation of the Crimean Peninsula and support for separatists in eastern Ukraine.

The conflict in eastern Ukraine between Kyiv's forces and Russia-backed separatists has killed more than 10,000 people since it erupted in April 2014.

Poroshenko said Trump supported a proposal to deploy UN peacekeepers "including on the uncontrolled part of the Ukraine-Russia border, which would prevent the possibility of penetration by Russian troops or Russian weapons."

*CORRECTION: This story has been amended to clarify the length of the talks between Trump and Poroshenko, according to the Ukrainian president.